Question: Simplify the following expression: $t = \dfrac{-4z^2 + 40z - 84}{z - 3} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ t =\dfrac{-4(z^2 - 10z + 21)}{z - 3} $ Then we factor the remaining polynomial: $z^2 {-10}z + {21} $ ${-3} {-7} = {-10}$ ${-3} \times {-7} = {21}$ $ (z {-3}) (z {-7}) $ This gives us a factored expression: $\dfrac{-4(z {-3}) (z {-7})}{z - 3}$ We can divide the numerator and denominator by $(z + 3)$ on condition that $z \neq 3$ Therefore $t = -4(z - 7); z \neq 3$